对流-扩散方程的hp-局部间断Galerkin有限元方法的最优L∞(H^1)误差估计  

Optimal L∞(H^1) error estimates of the hp-local discontinuous Galerkin finite element method for convection-diffusion equations

作　　者：由同顺[1] YOU Tong-shun(School of Math.Sci.,Nankai Univ.,Tianjin 300071,China)

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《高校应用数学学报（A辑）》2020年第1期40-48,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：通过使用Arnold等人和Perugia等人对于椭圆问题引入的提升算子方法以及不同的处理非线性对流项的方法,得到了对流-扩散方程的hp-局部间断Galerkin有限元(hp-LDG)方法的最优L∞(H^1)误差估计.对于非线性Burgers方程进行了数值试验,计算结果验证了文中得到的理论结果.The main purpose of the paper is to analyze optimal L∞(H^1)error estimates of the hp-local discontinuous Galerkin finite element(hp-LDG)method for convection-diffusion equations.By using the lifting operator method introduced by Arnold et al.and Perugia et al.for elliptic problems and di®erent method for dealting with nonlinear convection terms,the optimal L∞(H^1)error estimates of hp-LDG method for the convection-diffusion problems are obtained.The paper also presents the numerical experiments for the nonlinear Burgers equation.The numerical results verify the theoretical results obtained in this paper.

关 键 词：对流-扩散方程 hp-LDG方法 提升算子 误差分析 

分 类 号：O241.8[理学—计算数学]